Submission date: 1 April 2017

Abstract:

We define two families of expansions of (Z,+,0) by unary predicates, and prove that their theories are superstable of U-rank ω. The first family consists of expansions (Z,+,0,A), where A is an infinite subset of a finitely generated multiplicative submonoid of N. Using this result, we also prove stability for the expansion of (Z,+,0) by all unary predicates of the form {q^n:n in N} for some q in N, q ≥ 2. The second family considers sets A ⊆ N which grow asymptotically close to a Q-linearly independent increasing sequence (λ_n)_{n=0}^∞ ⊆ R^+ such that { λ_n / λ_m : m ≤ n} is closed and discrete.

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Full text arXiv 1704.00105: pdf, ps.